1. Technical Field
The present disclosure is directed to FM demodulation and, in particular, FM demodulation having an extended threshold using an arcsin demodulator.
2. Description of the Related Art
Frequency modulation (FM) is a common method of encoding information. FM signals can generally be represented by the equationS(t)=Ac cos(ωct+φ(t))
where Ac is the amplitude, ωc is the carrier frequency in radians, and φ(t) is the information signal. The information signal can be written as
      φ    ⁡          (      t      )        =      2    ⁢    π    ⁢                  ⁢          k      f        ⁢                  ∫        0        t            ⁢                        m          ⁡                      (            τ            )                          ⁢                  ⅆ          τ                    
where m(t) is the modulating signal, and kf is constant and equal to the peak frequency deviation fd when m(t)=1. The modulation index, β, can be written as
  β  =                    Peak        ⁢                                  ⁢        RF        ⁢                                  ⁢        frequency        ⁢                                  ⁢        deviation                    Maximum        ⁢                                  ⁢        Modulating        ⁢                                  ⁢        baseband        ⁢                                  ⁢        frequency              =                            f          d                          f          max                    .      
A common problem with FM demodulation, especially in mobile FM radios, such as those in a vehicle, is that the signal strength can vary significantly as the car moves, causing harsh sounds. In particular, when the FM receiver is too far from the broadcasting antenna, the signal strength can be drastically reduced, making it difficult or impossible for traditional FM demodulators to function. Another problem occurs when the FM signal is reflected off surfaces. When this occurs, the FM receiver will receive two signals simultaneously, one directly from the broadcasting antenna, and another that has been reflected off a nearby surface, such as a building. The reflected signal may be out of phase with the direct signal because of the additional distance traveled, resulting in destructive interference. This destructive interference reduces the strength of the signal that is received at the FM demodulator. One issue associated with these circumstances in particular is the FM threshold effect, which can occur when the amplitude of the noise is comparable to or higher than the amplitude of the FM signal itself. When this occurs, demodulation of the signal rapidly breaks down.
The threshold effect can be seen in FIG. 1, where the signal-to-noise ratio (S/N or SNR) is generally linear for higher levels of carrier-to-noise ratio (p), but at a certain threshold point, the signal-to-noise ratio has a dramatic downward turn. To the left of this threshold point, the FM demodulator rapidly deteriorates.
The output signal-to-noise ratio of an FM system above the threshold region is given bySNRout=3β2(β+1)ρ.
However, when the threshold breakdown region is included, the output SNR is
      SNR    out    =                    3        ⁢                                  ⁢                              β            2                    ⁡                      (                          β              +              1                        )                          ⁢        ρ                    1        +                              24            π                    ⁢                      β            ⁡                          (                              β                +                1                            )                                ⁢                      ρⅇ                          (                              -                ρ                            )                                            .  
The carrier-to-noise ratio, ρ, is given by
  ρ  =            A      c      2              2      ⁢                          ⁢              N        0            ⁢              B                  I          ⁢                                          ⁢          F                    
where BIF is the bandwidth of the IF filter in the receiver and N0/2 is the two-sided power spectral density of the white noise.
As shown in FIG. 2, when the FM threshold effect occurs, the phase angle, θ(t), of the signal can abruptly increase or decrease by 2TT radians in a short period of time. This causes an impulse in the signal having an area of 2TT, and results in a “click” noise that can be heard by the user. The click noise generally indicates that the FM threshold has been reached, and the noise is greater than the signal.
There is a need for an FM demodulator that will extend the threshold beyond the current levels.